Bessel functions
>
f := BesselJ(nu+1,x)/BesselJ(nu,x);
>
pmint(f,x);
Maple has trouble with such integrands
>
int(f,x);
>
f := normal(nu*BesselJ(nu,x)/x - BesselJ(nu+1,x));
>
pmint(f,x);
Compare with Maple's answer
>
int(f,x);